Three New/Old Vertex–Degree–Based Topological Indices

Proceedings of the Romanian Academy - Series B: Chemistry

Journal of Chemistry, 2020

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

Journal of Mathematics

In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nanochemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic GHI , harmonic-geometric HGI , neighborhood harmonic-geometric NHGI , and neighborhood geometric-harmonic NGHI indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically.

Journal of Chemical Information and Modeling, 1998

Eigenvectors corresponding to the lowest eigenvalue of adjacency and distance matrices are used to generate new real-number local vertex invariants (LOVIs), by applying a Schultz-type algorithm. The intramolecular ordering of vertices was tested. From these LOVIs, several new topological indices have been defined and tested on the basis of intermolecular ordering of isomeric alkanes. Correlation with properties such as the normal boiling temperature and octane numbers have also been studied.

Journal of Mathematical Chemistry, 2009

Research on the topological indices based on end-vertex degrees of edges has been intensively rising recently. Randić index, one of the best-known topological indices in chemical graph theory, is belonging to this class of indices. In this paper, we introduce a novel topological index based on the end-vertex degrees of edges and its basic features are presented here. We named it as geometrical-arithmetic index (GA).

The Mj(m,n) and Mij(m,n) indices considered here are derived from the v m d n matrix by multiplication of its non-diagonal elements. A general characteristic of the Mj(m,n) and Mij(m,n) indices is the transition domain in the plane of exponents m and n, which is placed along the diagonal characterized by m = -n. Above this diagonal transition domain the values of the Mj(m,n) and Mij(m,n) indices of alkanes increase with the size of the molecule and decrease with branching, whereas the revers e is true below the diagonal. Correlation of tested Mj(m,n) and Mij(m,n) indices with the physicochemical properties of alkanes is better than r = 0.9 in 15 resp. 13 of 23 cases when alkanes from propane to octanes inclusive are considered, as well as in 12 resp. 8 of 24 cases when only octanes are taken into account. There is a number of Mj(m,n) and Mij(m,n) indices that have a regular sequence of isomers due to increasing branching. In the plane of exponents m and n they are positioned in th...

Journal of Physical & Theoretical Chemistry, 2015

It is well known that the chemical behavior of a compound is dependent upon the structure of its molecules. Quantitative structure -activity relationship (QSAR) studies and quantitative structureproperty relationship (QSPR) studies are active areas of chemical research that focus on the nature of this dependency. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indices for examination of structure-property relationship is Randic' index. In this study is represented the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the octanol-water partition coefficient (logP) of monocarboxylic acids (C 2 -C 20 ) are established, and then, some useful topological indices for examination of the structure-property relationship are presented.

Journal of Interdisciplinary Mathematics, 2022

To study the properties such as physical and chemical of compounds, the topological indices are introduced in chemical graph theory. These indices provide qualitative structure activity relationship (QSAR). Degree based topological indices are commonly used invariant in chemical graph theory. However, in this article, a new degree of vertices is introduced, called "deficiency degree". Further, we have computed five topological indices based on the deficiency degree like "deficient first Zagreb index, deficient generalized Randić index, deficient harmonic index, deficient inverse sum index, deficient augmented Zagreb index" for identified graphs using the M-polynomial of graph.

Journal of Physical & Theoretical Chemistry, 2007

The fact that the properties of a molecule are tightly connected to its structural characteristics is one of the fundamental concepts in chemistry. In this connection, graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. So , a novel method for computing the new descriptors to construct a quantitative relation between structure and properties is presented. At first, a brief review on the classical graph theories introduced and, then, the link with molecular similarity is drawn. In the applications section, molecular topological indices are calculated. Afterwards, the molecular descriptors, that include the necessary structural information for properly describtion of system are employed to derive a numerical correlation with thermodynamic properties. Finally, some useful topological indices for examination of the structure-property relationship are presented. In addition, the relationship between the Randic / , Wiener, Hosoya , Balaban and Schultz indices and Harary numbers and Distance matrix to the enthalpies of formation ( ) f o H ∆ , heat capacities, (Cp) , enthalpies of combustion ( ) c o H ∆ , enthalpies of vaporization ( ) vap H o ∆ and normal boiling points ( ) bpK for 10 2 C Cnormal alcohols is established.

Journal of Chemical Information and Modeling, 2007

The sequence of all paths p i of lengths i) 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Σ i p i 2 , and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q) Σ i p i 2 /(µ+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Σ i p i 1/2 , and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S) Σ i p i 1/2 /(µ+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D) Σ i {p i 1/2 /[i(µ+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A) Σ i {p i /[i(µ + 1)]}; and (v) the last TI with two square roots: Path-count index: P) Σ i {p i 1/2 / [i 1/2 (µ + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property. † Dedicated to Professor Nenad Trinajstić on the occasion of his 70th birthday.